Probing cosmology with astrophysical gravitational wave background

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The original goals of the research proposal have been already achieved. During the past 12 months I have worked on extensions of the proposed projects. I have completed a paper studying anisotropic gravitational-wave background originating from primordial black-hole binaries formed in the early universe, and have assessed the prospects of distinguishing the primordial and astrophysical origins of gravitational-wave binaries. Additionally, I have continued working on modeling the cross-correlations between resolved gravitation-wave sources and galaxies with the aim of testing gravity at cosmological scales, as well as establishing the origin of gravitational-wave binaries via measuring the linear bias of their spatial clustering.In addition to the main theme of the KAKENHI project, I have also worked on projects of indirect relevance to the main theme. Particularly, I have completed a paper exploring the prospects of generating magnetic fields in the early universe. The studied scenario is also relevant for gravitation-wave generation, and is of interest for future gravitational-wave experiments. I have also released a paper discussing possible tests of fundamental physics using GRBs, and have studied extensions of the LCDM model.I have completed research visits during which I have delivered invited talks based on the obtained results, as detailed at later sections of this report.